On the number of integer polynomials with multiplicatively dependent roots

被引：1

作者：

Dubickas, A. ^{[1
]}

Sha, M. ^{[2
]}

机构：

[1] Vilnius Univ, Inst Math, Fac Math & Informat, Naugarduko 24, LT-03225 Vilnius, Lithuania

[2] Macquarie Univ, Dept Comp, Sydney, NSW 2109, Australia

来源：

ACTA MATHEMATICA HUNGARICA | 2018年 / 154卷 / 02期

关键词：

multiplicative dependence; degenerate polynomial; generalized degenerate polynomial; CONJUGATE ALGEBRAIC-NUMBERS; REDUCIBLE POLYNOMIALS;

D O I：

10.1007/s10474-018-0788-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give some counting results on integer polynomials of fixed degree and bounded height whose distinct non-zero roots are multiplicatively dependent. These include sharp lower bounds, upper bounds and asymptotic formulas for various cases, although in general there is a logarithmic gap between lower and upper bounds.

引用

页码：402 / 428

页数：27

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